poj 3295 Tautology

Description

WFF 'N PROOF is a logic game played with dice. Each die has six faces representing some subset of the possible symbols K, A, N, C, E, p, q, r, s, t. A Well-formed formula (WFF) is any string of these symbols obeying the following rules:

• p, q, r, s, and t are WFFs
• if w is a WFF, Nwis a WFF
• if w and x are WFFs, Kwx, Awx, Cwx, and Ewx are WFFs.

The meaning of a WFF is defined as follows:

• p, q, r, s, and t are logical variables that may take on the value 0 (false) or 1 (true).
• K, A, N, C, E mean and, or, not, implies, and equals as defined in the truth table below.

Definitions of K, A, N, C, and E

w  x	Kwx	Awx	Nw	Cwx	Ewx
1  1	1	1	0	1	1
1  0	0	1	0	0	0
0  1	0	1	1	1	0
0  0	0	0	1	1	1

 

A tautology is a WFF that has value 1 (true) regardless of the values of its variables. For example, ApNp is a tautology because it is true regardless of the value of p. On the other hand, ApNq is not, because it has the value 0 for p=0, q=1.

You must determine whether or not a WFF is a tautology.

Input

Input consists of several test cases. Each test case is a single line containing a WFF with no more than 100 symbols. A line containing 0 follows the last case.

Output

For each test case, output a line containing tautology or not as appropriate.

Sample Input

ApNp
ApNq
0

Sample Output

tautology
not

32种情况，使用位运算效率很高

位运算,将整数的二进制某一位翻转可采用id^=(1<<x)(x代表要翻转的位置)

^异或   与0异或为本身 与1异或为取反

<<左移   >>右移

其他&按位与 |按位或 ~按位取反

#include <iostream>
using namespace std;
char str[101];
int pos;
bool judge( char str[], int value )
{
    pos++;
    switch ( str[pos] )
    {
    case 'p': return value&1;
    case 'q': return (value>>1)&1;
    case 'r': return (value>>2)&1;
    case 's': return (value>>3)&1;
    case 't': return (value>>4)&1;
    case 'K': return judge(str,value)&judge(str,value);
    case 'A': return judge(str,value)|judge(str,value);
    case 'N': return !judge(str,value);
    case 'C': return (!judge(str,value))|judge(str,value);
    case 'E': return judge(str,value)==judge(str,value);
    default:;
    }
}
int main()
{
    bool mark;
    while ( cin >> str && str[0] != '0' )
    {
        mark = true;
        for ( int i = 0; i < 32; i++ )
        {
            pos = -1;
            if ( !judge(str,i) ) 
            {
                mark = false; break;
            }
        }
        if ( mark ) cout << "tautology" << endl;
        else cout << "not" << endl;
    }
    return 0;
}